This is a phase I-II dose escalation study of 3'-Azido-2',3'-dideoxyuridine (AzdU), an orally administered nucleoside analog, in adults with HIV infection and between 200 and 400 CD4+ lymphocytes/mm3. This subset of HIV infected persons was selected to not include persons for who zidovudine (AZT) had been approved by the FDA. The purpose of the study is to establish a maximal tolerated dose of AzdU and in the process collect data on its potential anti-viral and immune-enhancing effects. The drug will be given for a 12-week period, with extensions based on safety and efficacy. Blood levels of AzdU will be obtained to establish its bioavailability and single-dose versus multiple-dose pharmacokinetics in humans. The importance of this study is that it assesses an antiviral drug for AIDS that may be less toxic but equally effective as AZT. The study has been fully enrolled as of July 1990.